I'm having the exact same problem! And it's discouraging that no one at AMD/ATI has addressed "pacomputer"'s problem in the last 6 months.
I've just put together a new computer with an "ASRock FM2A85X Extreme" motherboard and an A6-5400K APU from Newegg. I'm using an older (but completely functional) VGA monitor plugged into the VGA port. Just like pacomputer, the video output was totally stable as long as I was using the standard VGA driver, but as soon as I installed the Radeon driver, it started blanking out for 2 or 3 seconds at a time, randomly, and doing so several times a minute.
Like pacomputer, if I revert the device driver back to the standard VGA driver, the blanking stops.
At first, I thought (hoped) it was because I'd installed an older Radeon driver (8.947.0.0) from ASRock's driver disk that came with the motherboard, but when I connected the computer to the internet and downloaded the latest version (184.108.40.206), it had exactly the same problem.
I've tried changing the video resolution from the Monitor's preferred resolution (1280x1024) to other values, but that didn't make any difference. I've also tried changing the video refresh rate from 60Hz to 75Hz and that didn't make any difference either.
There are no error messages visible or on the Windows System Event logs.
The 2-or-3 seconds of black is just like what happens when the video output mode changes and it takes the monitor a couple of seconds to respond and resync, so it's 99% likely that this is an issue with the sync signals in the VGA output. And it has to be a bug in the Radeon video accelleration driver, because the standard VGA driver that ships with the Windows 7 install disk produces rock solid output with exactly the same hardware + monitor + cables.
I'm hoping that changing to a different monitor with a DVI input will fix the problem. (I don't have one on hand right now.) But if not, I'd have to say that this APU is defective and completely unusable!